Testing Lorentz force on a moving macroscopic charged conductor? Did anyone ever made an experiment with a moving macroscopic charged conductor in a magnetic field testing its deviation due to Lorentz force? I mean: what moves here is the massive charged conductor itself, not only the charges inside it. Would it be feasible with our technology? If it is then why does this force only appears in late 1800's in the scientific literature?
 A: A macroscopic object with charge $q$ will not experience a magnetic force of the form $${\bf F}=q(\bf v\times B)$$ if it were to pass through a magnetic field $\bf B$
And of course if there is an electric field, then we have the full form of the Lorentz (electromagnetic) force $${\bf F}=q(\bf E+ v\times B)$$
and charged particles experience a local electromagnetic force according to this equation. That is, this equation does not work for macroscopic objects.
If we wanted to extend the Lorentz force law to macroscopic objects,  we would need to take into account additional quantities like the polarization (density) $\bf P$ and
magnetization (density) $\bf M$ to be sources of the electromagnetic field and this can severely complicate the situation.
In such a case, the Lorentz force$^1$ (density) takes on a much different form $${\bf F} = (\rho_f −\nabla\cdot {\bf P}){\bf E} + ({\bf J_f}+ \frac{\partial {\bf P}}{\partial t})\times \mu_0{\bf H} − (\nabla\cdot {\bf M}){\bf H} − (\frac{\partial {\bf M}}{\partial t})\times \epsilon_0 {\bf E}$$
where $\rho_f$ and $\bf J_f$ are free charge and current densities respectively, where $${\bf B}= \mu_0 {\bf H} + \bf M$$
Note that the equation for the Lorentz force density requires many assumptions to be valid, and an explanation of this and a derivation can be found here. This equation has been tested, but for very simple systems and the experiment appears to be consistent with the equations.
$^1$ Note that many authors have many other forms to this equation depending on the setup, assumptions, boundary conditions etc., and the equation above for the electromagnetic force density is in the most general form.
